The generator matrix

 1  0  0  1  1  1  1  1  1 2X^2  1  1 2X^2+X  1  1  1  X 2X^2+X  1  1 X^2+X  1 2X  1 X^2+2X  1  1  1  0  1  1  1  X  1  1 2X^2+X  1  1 X^2 2X^2  1  1 2X^2+2X  1 2X^2+2X  1  1  1  1  1  1  1 X^2+2X  1  1 2X^2+X  1 X^2+2X  1  1 X^2 X^2  1  1  1 2X^2+X  X  1  1  1 2X 2X  1  1  1  1  1 X^2  1  1 X^2+2X  1  1  1  1 X^2+X  1
 0  1  0 2X^2  1 2X^2+1 2X^2+2  X  2  1 2X^2+2X+1 2X^2+2X+2  1 X^2 2X^2+X+2 X^2+2X+1  1 2X X^2+2X+2 2X  1 X^2+X  1 X^2+1  1 2X^2+X+1 X+2 X^2+X+1 2X X^2  0 2X+2  1 2X^2+1 X^2+2X  1 X^2+X+2 2X^2+X  1  1  1 X+1  0 X^2+2X  1 X^2+2 X^2+X 2X^2+2X+1 2X^2+2 X^2+2 2X X^2+X+1  1 X+1 2X^2+X  1 X^2+2X+2 X^2+2X  X X^2+X+2  1  X X^2+2 2X^2+X+2 X^2+2X+1  X X^2 2X^2+2X+1 X+2 X^2+X  1  1 2X^2  1 2X^2+1  0 2X+1  1 X^2+X+2 X^2+2 X^2+X 2X^2+1  X 2X^2+X+2 X^2+2X  1  0
 0  0  1 2X^2+2X+1 2X+1 2X^2 X^2+X+2 X+2 X^2+2X 2X^2+1 2X^2+2X+2 2X^2+1 2X^2+2 X^2+X 2X^2+X+2 X^2 X^2+1  1 2X^2+2X 2X+2  0 X^2+1 X^2+1 2X^2+X  2  1 X^2+X+1 X^2+2X+2  1 X^2+2X 2X^2+X+1 2X+2 X^2+X X+1 X^2+X 2X^2+X+1 X^2 X^2+2  X 2X^2+2X+2 2X^2+X+2 2X^2  1 X+2  X X^2+2X+1  X X+1 2X^2+X+1  0 2X 2X^2+X 2X+2 2X+1 2X^2+2X+2 X^2+2X+1 2X^2+2X+1  1 X+1  1 2X^2+X+2  1 2X^2+X 2X^2+2X X^2+2  1  1 2X^2+2X+1 X^2+2X+1 X^2+2X 2X^2+2X+1 2X^2 X^2+1 2X^2+2X+2 2X X^2+X X^2+1 X+1 2X^2+X+1  1  1 X^2+1 X^2  X  1  1 X^2

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+330x^167+498x^168+1812x^169+2478x^170+1376x^171+1968x^172+1932x^173+1268x^174+1440x^175+1212x^176+836x^177+1200x^178+1128x^179+366x^180+648x^181+522x^182+248x^183+222x^184+174x^185+20x^186+2x^201+2x^204

The gray image is a linear code over GF(3) with n=783, k=9 and d=501.
This code was found by Heurico 1.16 in 1.34 seconds.